2D–EM clustering approach for high-dimensional data through folding feature vectors

Alok Sharma, Piotr J. Kamola, Tatsuhiko Tsunoda

Clustering methods are becoming widely utilized in biomedical research where the volume and complexity of data is rapidly increasing. Unsupervised clustering of patient information can reveal distinct phenotype groups with different underlying mechanism, risk prognosis and treatment response. However, biological datasets are usually characterized by a combination of low sample number and very high dimensionality, something that is not adequately addressed by current algorithms. While the performance of the methods is satisfactory for low dimensional data, increasing number of features results in either deterioration of accuracy or inability to cluster. To tackle these challenges, new methodologies designed specifically for such data are needed. We present 2D-EM, a clustering algorithm approach designed for small sample size and high-dimensional datasets. To employ information corresponding to data distribution and facilitate visualization, the sample is folded into its two-dimension (2D) matrix form (or feature matrix). The maximum likelihood estimate is then estimated using a modified expectation-maximization (EM) algorithm. The 2D-EM methodology was benchmarked against several existing clustering methods using 6 medically-relevant transcriptome datasets. The percentage improvement of Rand score and adjusted Rand index compared to the best performing alternative method is up to 21.9% and 155.6%, respectively. To present the general utility of the 2D-EM method we also employed 2 methylome datasets, again showing superior performance relative to established methods. The 2D-EM algorithm was able to reproduce the groups in transcriptome and methylome data with high accuracy. This build confidence in the methods ability to uncover novel disease subtypes in new datasets. The design of 2D-EM algorithm enables it to handle a diverse set of challenging biomedical dataset and cluster with higher accuracy than established methods. MATLAB implementation of the tool can be freely accessed online ( http://www.riken.jp/en/research/labs/ims/med_sci_math or http://www.alok-ai-lab.com /).